Propagation of the \(L^{r}\) -norms for the Boltzmann equation has been of great interest in the community for quite some time, see for instance [1]}, [2]}, [3]}. In [3]} a complete study was presented addressing not only the \(L^r\) -propagation of solutions to the space homogeneous Boltzmann equation, for \(r\in (1,\infty )\) , but also the propagation of Sobolev norms and convergence toward equilibrium.
